Modelling of deformations of high strength concrete at elevated temperatures

A constitutive model for the analysis of deformations of concrete subject to transient temperature and pressures is proposed. In these severe conditions concrete structures experience spalling phenomenon, which is the violent or non-violent breaking off of layers or pieces of concrete from the surface of a structural element when it is exposed to high and rapidly rising temperatures. This process can lead to a loss of load-bearing capacity, trough a loss of section and a loss of protection to steel reinforcement. Many different form of spalling exist, but probably the most dangerous is explosive spalling, because it is sudden and capable to result in a general collapse of the structure.The constitutive model includes thermo-chemical and mechanical damage for taking into account the deterioration of the material due to mechanical loads, high temperatures and chemical changes and it is introduced into a general coupled mathematical model of hygro-thermo-chemomechanical behaviour of concrete structures.In this constitutive model the so called free thermal strains, which are the concrete strains during first heating, are decomposed in three main contributions: thermal dilatation strains (treated in a manner usual in thermomechanics), shrinkage strains (modelled by means of the effective stress principle) and thermo-chemical strains (which take into account for the thermo-chemical decomposition of the concrete and which are related to thermo-chemical damage). Thermo-mechanical strains occurring during first heating of concrete under load, known as LITS (Load Induced Thermal Strains), are also included in the framework of thermodynamics of porous media. The proposed model is applied to an illustrative example that demonstrates its capabilities.RésuméNous proposons un modèle pour l'étude des déformations du béton sous variations de température et pression. Dans ces conditions extrêmes, le béton subit l'écaillage qui est une rupture violente ou non de couches ou pièces de béton sur la surface d'éléments structurels soumis à haute température ou température augmentant rapidement. Ce fait peut produire une diminution de la capacité portante à travers une diminution de la section ou la perte de protection du maillage. Il y a différentes formes d'écaillage mais le plus dangereux est probablement l'écaillage explosif car il est sans préavis et entraîne l'écroulement de la structure.Le modèle constitutif inclut l'endommagement thermochimique et mécanique pour prendre en compte la détérioration du matériau due aux charges mécaniques, aux hautes températures et aux chargements chimiques.Tout ceci est introduit dans un modèle mathématique couplé pour la description du comportement hygrothermochimique et mécanique des structures en béton. Dans ce modèle constitutif, les déformations thermiques libres, c'est à dire les déformations dans le béton pendant le premier échauffement sont décomposés en trois parties: déformations dues à la dilatation thermique (traitées selon la manière habituelle de la thermomécanique), déformations dues au séchage (modèles à l'aide des contraintes effectives) et déformations thermochimiques (qui prennent en compte la décomposition thermochimique du béton et qui sont liées à l'endommagement thermochimique). Les déformations thermomécaniques qui ont lieu pendant le premier échauffement du béton sous charge, généralement connues sous le nom de LITS (Load Induced Thermal Strain) sont aussi inclues dans le cadre de la thermodynamique des milieux poreux. Le modèle proposé est appliqué à un exemple pour démontrer ses capacités.

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